$\bar B_s\to K$ semileptonic decay from an Omnès improved nonrelativistic quark model

Abstract

We study the $f^+$ form factor for the $\bar B_s\to K^+\ell^-\barν_\ell$ semileptonic decay in a nonrelativistic quark model. The valence quark contribution is supplemented with a $\bar B^*$-pole term that dominates the high $q^2$ region. To extend the quark model predictions from its region of applicability near $q^2_{\rm max}=(M_{B_s}-M_K)^2$, we use a multiply-subtracted Omnès dispersion relation. We fit the subtraction constants to a combined input from previous light cone sum rule results in the low $q^2$ region and the quark model results (valence plus $\bar B^*$-pole) in the high $q^2$ region. From this analysis, we obtain $Γ(\bar B_s\to K^+\ell^-\barν_\ell)=(5.47^{+0.54}_{-0.46})|V_{ub}|^2\times 10^{-9}\,{\rm MeV}$, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.

4 latex pages, 3 figures, 1 table. Talk presented at the "XI International Conference on Hyperons, Charm and Beauty Hadrons (BEACH 2014)", Birmingham (U.K.), July 2014